Question

Find the value of k if 2x²+kx+3=0 has two equal roots

Answer 1

Answer: k = ± 2√6

Step-by-step explanation:

To find: the value of k

Given quadratic equation: 2x² + kx + 3 = 0

Thus,

Discriminant: D = b² - 4ac = 0

Comparing 2x² + kx + 3 = 0 with the equation: ax² + bx + c = 0; we get,

a = 2, b = k and c = 3

Thus, D = (k)² - 4 ×(2) × (3) = 0

=> k² - 24 = 0

k² = 24

k = √24

k = +2√6 or -2√6

Thus, the value of k is ± 2√6.

Answer 2

AnswEr:

Values of k are 2√6 and -2√6

ExplanaTion:

It is given that, polynomial p(x) = 2x² + kx + 3 = 0 has equal roots, so Discriminant must be equal to zero.

Comparing the given Polynomial p(x) with general equation, i.e ax² + bx + c = 0, we get,

• a = 2
• b = k
• c = 3

$\large{\boxed{\green{\sf{b^2 - 4ac\:=\:0}}}}$

Putting the values,

$\implies$ (k)² - 4 (2) (3) = 0

$\implies$ k² - 24 = 0

$\implies$ k² = 24

$\implies$ k = ±√24

$\implies$ k = 2√6 and -2√6

Hence, Values of k are 2√6 and -2√6